isl_constraint.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  * Copyright 2010      INRIA Saclay
   4  *
   5  * Use of this software is governed by the GNU LGPLv2.1 license
   6  *
   7  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   8  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   9  * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
  10  * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
  11  */
  12
  13 #include <isl_map_private.h>
  14 #include <isl_constraint_private.h>
  15 #include <isl_dim_private.h>
  16 #include <isl_div_private.h>
  17 #include <isl/seq.h>
  18 #include <isl_aff_private.h>
  19
  20 isl_ctx *isl_constraint_get_ctx(__isl_keep isl_constraint *c)
  21 {
  22         return c ? c->ctx : NULL;
  23 }
  24
  25 static unsigned n(struct isl_constraint *c, enum isl_dim_type type)
  26 {
  27         return isl_basic_map_dim(c->bmap, type);
  28 }
  29
  30 static unsigned offset(struct isl_constraint *c, enum isl_dim_type type)
  31 {
  32         struct isl_dim *dim = c->bmap->dim;
  33         switch (type) {
  34         case isl_dim_param:     return 1;
  35         case isl_dim_in:        return 1 + dim->nparam;
  36         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
  37         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
  38         default:                return 0;
  39         }
  40 }
  41
  42 static unsigned basic_map_offset(__isl_keep isl_basic_map *bmap,
  43                                                         enum isl_dim_type type)
  44 {
  45         return type == isl_dim_div ? 1 + isl_dim_total(bmap->dim)
  46                                    : 1 + isl_dim_offset(bmap->dim, type);
  47 }
  48
  49 static unsigned basic_set_offset(struct isl_basic_set *bset,
  50                                                         enum isl_dim_type type)
  51 {
  52         struct isl_dim *dim = bset->dim;
  53         switch (type) {
  54         case isl_dim_param:     return 1;
  55         case isl_dim_in:        return 1 + dim->nparam;
  56         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
  57         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
  58         default:                return 0;
  59         }
  60 }
  61
  62 struct isl_constraint *isl_basic_map_constraint(struct isl_basic_map *bmap,
  63         isl_int **line)
  64 {
  65         struct isl_constraint *constraint;
  66
  67         if (!bmap || !line)
  68                 goto error;
  69
  70         constraint = isl_alloc_type(bmap->ctx, struct isl_constraint);
  71         if (!constraint)
  72                 goto error;
  73
  74         constraint->ctx = bmap->ctx;
  75         isl_ctx_ref(constraint->ctx);
  76         constraint->ref = 1;
  77         constraint->bmap = bmap;
  78         constraint->line = line;
  79
  80         return constraint;
  81 error:
  82         isl_basic_map_free(bmap);
  83         return NULL;
  84 }
  85
  86 struct isl_constraint *isl_basic_set_constraint(struct isl_basic_set *bset,
  87         isl_int **line)
  88 {
  89         return isl_basic_map_constraint((struct isl_basic_map *)bset, line);
  90 }
  91
  92 struct isl_constraint *isl_equality_alloc(struct isl_dim *dim)
  93 {
  94         struct isl_basic_map *bmap;
  95
  96         if (!dim)
  97                 return NULL;
  98
  99         bmap = isl_basic_map_alloc_dim(dim, 0, 1, 0);
 100         if (!bmap)
 101                 return NULL;
 102
 103         isl_basic_map_alloc_equality(bmap);
 104         isl_seq_clr(bmap->eq[0], 1 + isl_basic_map_total_dim(bmap));
 105         return isl_basic_map_constraint(bmap, &bmap->eq[0]);
 106 }
 107
 108 struct isl_constraint *isl_inequality_alloc(struct isl_dim *dim)
 109 {
 110         struct isl_basic_map *bmap;
 111
 112         if (!dim)
 113                 return NULL;
 114
 115         bmap = isl_basic_map_alloc_dim(dim, 0, 0, 1);
 116         if (!bmap)
 117                 return NULL;
 118
 119         isl_basic_map_alloc_inequality(bmap);
 120         isl_seq_clr(bmap->ineq[0], 1 + isl_basic_map_total_dim(bmap));
 121         return isl_basic_map_constraint(bmap, &bmap->ineq[0]);
 122 }
 123
 124 struct isl_constraint *isl_constraint_dup(struct isl_constraint *c)
 125 {
 126         struct isl_basic_map *bmap;
 127         int i;
 128         int eq;
 129
 130         if (!c)
 131                 return NULL;
 132
 133         eq = c->line < c->bmap->eq + c->bmap->n_eq;
 134         i = eq ? c->line - c->bmap->eq : c->line - c->bmap->ineq;
 135         bmap = isl_basic_map_copy(c->bmap);
 136         if (!bmap)
 137                 return NULL;
 138         return isl_basic_map_constraint(bmap, eq ? bmap->eq + i : bmap->ineq + i);
 139 }
 140
 141 struct isl_constraint *isl_constraint_cow(struct isl_constraint *c)
 142 {
 143         if (!c)
 144                 return NULL;
 145
 146         if (c->ref == 1)
 147                 return c;
 148         c->ref--;
 149         return isl_constraint_dup(c);
 150 }
 151
 152 struct isl_constraint *isl_constraint_copy(struct isl_constraint *constraint)
 153 {
 154         if (!constraint)
 155                 return NULL;
 156
 157         constraint->ref++;
 158         return constraint;
 159 }
 160
 161 void isl_constraint_free(struct isl_constraint *c)
 162 {
 163         if (!c)
 164                 return;
 165
 166         if (--c->ref > 0)
 167                 return;
 168
 169         isl_basic_map_free(c->bmap);
 170         isl_ctx_deref(c->ctx);
 171         free(c);
 172 }
 173
 174 int isl_basic_map_foreach_constraint(__isl_keep isl_basic_map *bmap,
 175         int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
 176 {
 177         int i;
 178         struct isl_constraint *c;
 179
 180         if (!bmap)
 181                 return -1;
 182
 183         isl_assert(bmap->ctx, ISL_F_ISSET(bmap, ISL_BASIC_MAP_FINAL),
 184                         return -1);
 185
 186         for (i = 0; i < bmap->n_eq; ++i) {
 187                 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
 188                                                 &bmap->eq[i]);
 189                 if (!c)
 190                         return -1;
 191                 if (fn(c, user) < 0)
 192                         return -1;
 193         }
 194
 195         for (i = 0; i < bmap->n_ineq; ++i) {
 196                 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
 197                                                 &bmap->ineq[i]);
 198                 if (!c)
 199                         return -1;
 200                 if (fn(c, user) < 0)
 201                         return -1;
 202         }
 203
 204         return 0;
 205 }
 206
 207 int isl_basic_set_foreach_constraint(__isl_keep isl_basic_set *bset,
 208         int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
 209 {
 210         return isl_basic_map_foreach_constraint((isl_basic_map *)bset, fn, user);
 211 }
 212
 213 int isl_constraint_is_equal(struct isl_constraint *constraint1,
 214         struct isl_constraint *constraint2)
 215 {
 216         if (!constraint1 || !constraint2)
 217                 return 0;
 218         return constraint1->bmap == constraint2->bmap &&
 219                constraint1->line == constraint2->line;
 220 }
 221
 222 struct isl_basic_map *isl_basic_map_add_constraint(
 223         struct isl_basic_map *bmap, struct isl_constraint *constraint)
 224 {
 225         if (!bmap || !constraint)
 226                 goto error;
 227
 228         isl_assert(constraint->ctx,
 229                 isl_dim_equal(bmap->dim, constraint->bmap->dim), goto error);
 230
 231         bmap = isl_basic_map_intersect(bmap,
 232                                 isl_basic_map_from_constraint(constraint));
 233         return bmap;
 234 error:
 235         isl_basic_map_free(bmap);
 236         isl_constraint_free(constraint);
 237         return NULL;
 238 }
 239
 240 struct isl_basic_set *isl_basic_set_add_constraint(
 241         struct isl_basic_set *bset, struct isl_constraint *constraint)
 242 {
 243         return (struct isl_basic_set *)
 244                 isl_basic_map_add_constraint((struct isl_basic_map *)bset,
 245                                                 constraint);
 246 }
 247
 248 __isl_give isl_map *isl_map_add_constraint(__isl_take isl_map *map,
 249         __isl_take isl_constraint *constraint)
 250 {
 251         isl_basic_map *bmap;
 252
 253         bmap = isl_basic_map_from_constraint(constraint);
 254         map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
 255
 256         return map;
 257 }
 258
 259 __isl_give isl_set *isl_set_add_constraint(__isl_take isl_set *set,
 260         __isl_take isl_constraint *constraint)
 261 {
 262         return isl_map_add_constraint(set, constraint);
 263 }
 264
 265 struct isl_constraint *isl_constraint_add_div(struct isl_constraint *constraint,
 266         struct isl_div *div, int *pos)
 267 {
 268         if (!constraint || !div)
 269                 goto error;
 270
 271         isl_assert(constraint->ctx,
 272             isl_dim_equal(div->bmap->dim, constraint->bmap->dim), goto error);
 273         isl_assert(constraint->ctx,
 274             constraint->bmap->n_eq + constraint->bmap->n_ineq == 1, goto error);
 275
 276         constraint->bmap = isl_basic_map_cow(constraint->bmap);
 277         constraint->bmap = isl_basic_map_extend_dim(constraint->bmap,
 278                                 isl_dim_copy(constraint->bmap->dim), 1, 0, 0);
 279         if (!constraint->bmap)
 280                 goto error;
 281         constraint->line = &constraint->bmap->ineq[0];
 282         *pos = isl_basic_map_alloc_div(constraint->bmap);
 283         if (*pos < 0)
 284                 goto error;
 285         isl_seq_cpy(constraint->bmap->div[*pos], div->line[0],
 286                         1 + 1 + isl_basic_map_total_dim(constraint->bmap));
 287         isl_div_free(div);
 288         return constraint;
 289 error:
 290         isl_constraint_free(constraint);
 291         isl_div_free(div);
 292         return NULL;
 293 }
 294
 295 __isl_give isl_dim *isl_constraint_get_dim(
 296         __isl_keep isl_constraint *constraint)
 297 {
 298         return constraint ? isl_basic_map_get_dim(constraint->bmap) : NULL;
 299 }
 300
 301 int isl_constraint_dim(struct isl_constraint *constraint,
 302         enum isl_dim_type type)
 303 {
 304         if (!constraint)
 305                 return -1;
 306         return n(constraint, type);
 307 }
 308
 309 int isl_constraint_involves_dims(__isl_keep isl_constraint *constraint,
 310         enum isl_dim_type type, unsigned first, unsigned n)
 311 {
 312         if (!constraint)
 313                 return -1;
 314
 315         if (first + n > isl_basic_set_dim(constraint->bmap, type))
 316                 isl_die(constraint->ctx, isl_error_invalid,
 317                         "index out of bounds", return -1);
 318
 319         first += isl_basic_map_offset(constraint->bmap, type);
 320
 321         if (isl_seq_first_non_zero(constraint->line[0] + first, n) >= 0)
 322                 return 1;
 323
 324         return 0;
 325 }
 326
 327 const char *isl_constraint_get_dim_name(__isl_keep isl_constraint *constraint,
 328         enum isl_dim_type type, unsigned pos)
 329 {
 330         return constraint ?
 331             isl_basic_map_get_dim_name(constraint->bmap, type, pos) : NULL;
 332 }
 333
 334 void isl_constraint_get_constant(struct isl_constraint *constraint, isl_int *v)
 335 {
 336         if (!constraint)
 337                 return;
 338         isl_int_set(*v, constraint->line[0][0]);
 339 }
 340
 341 void isl_constraint_get_coefficient(struct isl_constraint *constraint,
 342         enum isl_dim_type type, int pos, isl_int *v)
 343 {
 344         if (!constraint)
 345                 return;
 346
 347         isl_assert(constraint->ctx, pos < n(constraint, type), return);
 348         isl_int_set(*v, constraint->line[0][offset(constraint, type) + pos]);
 349 }
 350
 351 struct isl_div *isl_constraint_div(struct isl_constraint *constraint, int pos)
 352 {
 353         if (!constraint)
 354                 return NULL;
 355
 356         isl_assert(constraint->ctx, pos < n(constraint, isl_dim_div),
 357                         return NULL);
 358         isl_assert(constraint->ctx,
 359                 !isl_int_is_zero(constraint->bmap->div[pos][0]), return NULL);
 360         return isl_basic_map_div(isl_basic_map_copy(constraint->bmap), pos);
 361 }
 362
 363 void isl_constraint_set_constant(struct isl_constraint *constraint, isl_int v)
 364 {
 365         if (!constraint)
 366                 return;
 367         isl_int_set(constraint->line[0][0], v);
 368 }
 369
 370 void isl_constraint_set_constant_si(__isl_keep isl_constraint *constraint,
 371         int v)
 372 {
 373         if (!constraint)
 374                 return;
 375         isl_int_set_si(constraint->line[0][0], v);
 376 }
 377
 378 void isl_constraint_set_coefficient(struct isl_constraint *constraint,
 379         enum isl_dim_type type, int pos, isl_int v)
 380 {
 381         if (!constraint)
 382                 return;
 383
 384         isl_assert(constraint->ctx, pos < n(constraint, type), return);
 385         isl_int_set(constraint->line[0][offset(constraint, type) + pos], v);
 386 }
 387
 388 void isl_constraint_set_coefficient_si(__isl_keep isl_constraint *constraint,
 389         enum isl_dim_type type, int pos, int v)
 390 {
 391         if (!constraint)
 392                 return;
 393
 394         isl_assert(constraint->ctx, pos < n(constraint, type), return);
 395         isl_int_set_si(constraint->line[0][offset(constraint, type) + pos], v);
 396 }
 397
 398 void isl_constraint_clear(struct isl_constraint *constraint)
 399 {
 400         unsigned total;
 401
 402         if (!constraint)
 403                 return;
 404         total = isl_basic_map_total_dim(constraint->bmap);
 405         isl_seq_clr(constraint->line[0], 1 + total);
 406 }
 407
 408 /* Check whether the two basic maps have identical divs in the same order.
 409  */
 410 static int equal_divs(__isl_keep isl_basic_map *bmap1,
 411         __isl_keep isl_basic_map *bmap2)
 412 {
 413         int i;
 414         unsigned total;
 415
 416         if (!isl_basic_map_divs_known(bmap1))
 417                 return 0;
 418         if (!isl_basic_map_divs_known(bmap2))
 419                 return 0;
 420         if (bmap1->n_div != bmap2->n_div)
 421                 return 0;
 422
 423         total = isl_basic_map_total_dim(bmap1);
 424         for (i = 0; i < bmap1->n_div; ++i)
 425                 if (!isl_seq_eq(bmap1->div[i], bmap2->div[i], 2 + total))
 426                         return 0;
 427
 428         return 1;
 429 }
 430
 431 /* Drop any constraint from "bset" that is identical to "constraint".
 432  * In particular, this means that the local spaces of "bset" and
 433  * "constraint" need to be the same.
 434  *
 435  * Since the given constraint may actually be a pointer into the bset,
 436  * we have to be careful not to reorder the constraints as the user
 437  * may be holding on to other constraints from the same bset.
 438  * This should be cleaned up when the internal representation of
 439  * isl_constraint is changed to use isl_aff.
 440  */
 441 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
 442         __isl_take isl_basic_set *bset, __isl_take isl_constraint *constraint)
 443 {
 444         int i;
 445         unsigned n;
 446         isl_int **row;
 447         unsigned total;
 448
 449         if (!bset || !constraint)
 450                 goto error;
 451
 452         if (!isl_dim_equal(bset->dim, constraint->bmap->dim))
 453                 isl_die(bset->ctx, isl_error_invalid,
 454                         "spaces don't match", goto error);
 455
 456         if (bset != constraint->bmap && !equal_divs(bset, constraint->bmap)) {
 457                 isl_constraint_free(constraint);
 458                 return bset;
 459         }
 460
 461         if (isl_constraint_is_equality(constraint)) {
 462                 n = bset->n_eq;
 463                 row = bset->eq;
 464         } else {
 465                 n = bset->n_ineq;
 466                 row = bset->ineq;
 467         }
 468
 469         total = isl_basic_map_total_dim(constraint->bmap);
 470         for (i = 0; i < n; ++i)
 471                 if (isl_seq_eq(row[i], constraint->line[0], 1 + total))
 472                         isl_seq_clr(row[i], 1 + total);
 473
 474         isl_constraint_free(constraint);
 475         return bset;
 476 error:
 477         isl_constraint_free(constraint);
 478         isl_basic_set_free(bset);
 479         return NULL;
 480 }
 481
 482 struct isl_constraint *isl_constraint_negate(struct isl_constraint *constraint)
 483 {
 484         unsigned total;
 485
 486         if (!constraint)
 487                 return NULL;
 488
 489         isl_assert(constraint->ctx, !isl_constraint_is_equality(constraint),
 490                         goto error);
 491         isl_assert(constraint->ctx, constraint->bmap->ref == 1, goto error);
 492         total = isl_basic_map_total_dim(constraint->bmap);
 493         isl_seq_neg(constraint->line[0], constraint->line[0], 1 + total);
 494         isl_int_sub_ui(constraint->line[0][0], constraint->line[0][0], 1);
 495         ISL_F_CLR(constraint->bmap, ISL_BASIC_MAP_NORMALIZED);
 496         return constraint;
 497 error:
 498         isl_constraint_free(constraint);
 499         return NULL;
 500 }
 501
 502 int isl_constraint_is_equality(struct isl_constraint *constraint)
 503 {
 504         if (!constraint)
 505                 return -1;
 506         return constraint->line >= constraint->bmap->eq;
 507 }
 508
 509 int isl_constraint_is_div_constraint(__isl_keep isl_constraint *constraint)
 510 {
 511         int i;
 512
 513         if (!constraint)
 514                 return -1;
 515         if (isl_constraint_is_equality(constraint))
 516                 return 0;
 517         for (i = 0; i < constraint->bmap->n_div; ++i) {
 518                 if (isl_int_is_zero(constraint->bmap->div[i][0]))
 519                         continue;
 520                 if (isl_basic_map_is_div_constraint(constraint->bmap,
 521                                         constraint->line[0], i))
 522                         return 1;
 523         }
 524
 525         return 0;
 526 }
 527
 528 /* We manually set ISL_BASIC_SET_FINAL instead of calling
 529  * isl_basic_map_finalize because we want to keep the position
 530  * of the divs and we therefore do not want to throw away redundant divs.
 531  * This is arguably a bit fragile.
 532  */
 533 __isl_give isl_basic_map *isl_basic_map_from_constraint(
 534         __isl_take isl_constraint *constraint)
 535 {
 536         int k;
 537         struct isl_basic_map *bmap;
 538         isl_int *c;
 539         unsigned total;
 540
 541         if (!constraint)
 542                 return NULL;
 543
 544         if (constraint->bmap->n_eq == 1 && constraint->bmap->n_ineq == 0) {
 545                 bmap = isl_basic_map_copy(constraint->bmap);
 546                 isl_constraint_free(constraint);
 547                 return bmap;
 548         }
 549
 550         bmap = isl_basic_map_universe_like(constraint->bmap);
 551         bmap = isl_basic_map_align_divs(bmap, constraint->bmap);
 552         bmap = isl_basic_map_cow(bmap);
 553         bmap = isl_basic_map_extend_constraints(bmap, 1, 1);
 554         if (isl_constraint_is_equality(constraint)) {
 555                 k = isl_basic_map_alloc_equality(bmap);
 556                 if (k < 0)
 557                         goto error;
 558                 c = bmap->eq[k];
 559         }
 560         else {
 561                 k = isl_basic_map_alloc_inequality(bmap);
 562                 if (k < 0)
 563                         goto error;
 564                 c = bmap->ineq[k];
 565         }
 566         total = isl_basic_map_total_dim(bmap);
 567         isl_seq_cpy(c, constraint->line[0], 1 + total);
 568         isl_constraint_free(constraint);
 569         if (bmap)
 570                 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
 571         return bmap;
 572 error:
 573         isl_constraint_free(constraint);
 574         isl_basic_map_free(bmap);
 575         return NULL;
 576 }
 577
 578 struct isl_basic_set *isl_basic_set_from_constraint(
 579         struct isl_constraint *constraint)
 580 {
 581         if (!constraint)
 582                 return NULL;
 583
 584         isl_assert(constraint->ctx,n(constraint, isl_dim_in) == 0, goto error);
 585         return (isl_basic_set *)isl_basic_map_from_constraint(constraint);
 586 error:
 587         isl_constraint_free(constraint);
 588         return NULL;
 589 }
 590
 591 int isl_basic_map_has_defining_equality(
 592         __isl_keep isl_basic_map *bmap, enum isl_dim_type type, int pos,
 593         __isl_give isl_constraint **c)
 594 {
 595         int i;
 596         unsigned offset;
 597         unsigned total;
 598
 599         if (!bmap)
 600                 return -1;
 601         offset = basic_map_offset(bmap, type);
 602         total = isl_basic_map_total_dim(bmap);
 603         isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
 604         for (i = 0; i < bmap->n_eq; ++i)
 605                 if (!isl_int_is_zero(bmap->eq[i][offset + pos]) &&
 606                     isl_seq_first_non_zero(bmap->eq[i]+offset+pos+1,
 607                                            1+total-offset-pos-1) == -1) {
 608                         *c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
 609                                                                 &bmap->eq[i]);
 610                         return 1;
 611                 }
 612         return 0;
 613 }
 614
 615 int isl_basic_set_has_defining_equality(
 616         __isl_keep isl_basic_set *bset, enum isl_dim_type type, int pos,
 617         __isl_give isl_constraint **c)
 618 {
 619         return isl_basic_map_has_defining_equality((isl_basic_map *)bset,
 620                                                     type, pos, c);
 621 }
 622
 623 int isl_basic_set_has_defining_inequalities(
 624         struct isl_basic_set *bset, enum isl_dim_type type, int pos,
 625         struct isl_constraint **lower,
 626         struct isl_constraint **upper)
 627 {
 628         int i, j;
 629         unsigned offset;
 630         unsigned total;
 631         isl_int m;
 632         isl_int **lower_line, **upper_line;
 633
 634         if (!bset)
 635                 return -1;
 636         offset = basic_set_offset(bset, type);
 637         total = isl_basic_set_total_dim(bset);
 638         isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
 639         isl_int_init(m);
 640         for (i = 0; i < bset->n_ineq; ++i) {
 641                 if (isl_int_is_zero(bset->ineq[i][offset + pos]))
 642                         continue;
 643                 if (isl_int_is_one(bset->ineq[i][offset + pos]))
 644                         continue;
 645                 if (isl_int_is_negone(bset->ineq[i][offset + pos]))
 646                         continue;
 647                 if (isl_seq_first_non_zero(bset->ineq[i]+offset+pos+1,
 648                                                 1+total-offset-pos-1) != -1)
 649                         continue;
 650                 for (j = i + 1; j < bset->n_ineq; ++j) {
 651                         if (!isl_seq_is_neg(bset->ineq[i]+1, bset->ineq[j]+1,
 652                                             total))
 653                                 continue;
 654                         isl_int_add(m, bset->ineq[i][0], bset->ineq[j][0]);
 655                         if (isl_int_abs_ge(m, bset->ineq[i][offset+pos]))
 656                                 continue;
 657
 658                         if (isl_int_is_pos(bset->ineq[i][offset+pos])) {
 659                                 lower_line = &bset->ineq[i];
 660                                 upper_line = &bset->ineq[j];
 661                         } else {
 662                                 lower_line = &bset->ineq[j];
 663                                 upper_line = &bset->ineq[i];
 664                         }
 665                         *lower = isl_basic_set_constraint(
 666                                         isl_basic_set_copy(bset), lower_line);
 667                         *upper = isl_basic_set_constraint(
 668                                         isl_basic_set_copy(bset), upper_line);
 669                         isl_int_clear(m);
 670                         return 1;
 671                 }
 672         }
 673         *lower = NULL;
 674         *upper = NULL;
 675         isl_int_clear(m);
 676         return 0;
 677 }
 678
 679 /* Given two constraints "a" and "b" on the variable at position "abs_pos"
 680  * (in "a" and "b"), add a constraint to "bset" that ensures that the
 681  * bound implied by "a" is (strictly) larger than the bound implied by "b".
 682  *
 683  * If both constraints imply lower bounds, then this means that "a" is
 684  * active in the result.
 685  * If both constraints imply upper bounds, then this means that "b" is
 686  * active in the result.
 687  */
 688 static __isl_give isl_basic_set *add_larger_bound_constraint(
 689         __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
 690         unsigned abs_pos, int strict)
 691 {
 692         int k;
 693         isl_int t;
 694         unsigned total;
 695
 696         k = isl_basic_set_alloc_inequality(bset);
 697         if (k < 0)
 698                 goto error;
 699
 700         total = isl_basic_set_dim(bset, isl_dim_all);
 701
 702         isl_int_init(t);
 703         isl_int_neg(t, b[1 + abs_pos]);
 704
 705         isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
 706         isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
 707                 t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
 708                 total - abs_pos);
 709
 710         if (strict)
 711                 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
 712
 713         isl_int_clear(t);
 714
 715         return bset;
 716 error:
 717         isl_basic_set_free(bset);
 718         return NULL;
 719 }
 720
 721 /* Add constraints to "context" that ensure that "u" is the smallest
 722  * (and therefore active) upper bound on "abs_pos" in "bset" and return
 723  * the resulting basic set.
 724  */
 725 static __isl_give isl_basic_set *set_smallest_upper_bound(
 726         __isl_keep isl_basic_set *context,
 727         __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
 728 {
 729         int j;
 730
 731         context = isl_basic_set_copy(context);
 732         context = isl_basic_set_cow(context);
 733
 734         context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);
 735
 736         for (j = 0; j < bset->n_ineq; ++j) {
 737                 if (j == u)
 738                         continue;
 739                 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
 740                         continue;
 741                 context = add_larger_bound_constraint(context,
 742                         bset->ineq[j], bset->ineq[u], abs_pos, j > u);
 743         }
 744
 745         context = isl_basic_set_simplify(context);
 746         context = isl_basic_set_finalize(context);
 747
 748         return context;
 749 }
 750
 751 /* Add constraints to "context" that ensure that "u" is the largest
 752  * (and therefore active) upper bound on "abs_pos" in "bset" and return
 753  * the resulting basic set.
 754  */
 755 static __isl_give isl_basic_set *set_largest_lower_bound(
 756         __isl_keep isl_basic_set *context,
 757         __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
 758 {
 759         int j;
 760
 761         context = isl_basic_set_copy(context);
 762         context = isl_basic_set_cow(context);
 763
 764         context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);
 765
 766         for (j = 0; j < bset->n_ineq; ++j) {
 767                 if (j == l)
 768                         continue;
 769                 if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
 770                         continue;
 771                 context = add_larger_bound_constraint(context,
 772                         bset->ineq[l], bset->ineq[j], abs_pos, j > l);
 773         }
 774
 775         context = isl_basic_set_simplify(context);
 776         context = isl_basic_set_finalize(context);
 777
 778         return context;
 779 }
 780
 781 static int foreach_upper_bound(__isl_keep isl_basic_set *bset,
 782         enum isl_dim_type type, unsigned abs_pos,
 783         __isl_take isl_basic_set *context, int n_upper,
 784         int (*fn)(__isl_take isl_constraint *lower,
 785                   __isl_take isl_constraint *upper,
 786                   __isl_take isl_basic_set *bset, void *user), void *user)
 787 {
 788         isl_basic_set *context_i;
 789         isl_constraint *upper = NULL;
 790         int i;
 791
 792         for (i = 0; i < bset->n_ineq; ++i) {
 793                 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
 794                         continue;
 795
 796                 context_i = set_smallest_upper_bound(context, bset,
 797                                                         abs_pos, n_upper, i);
 798                 if (isl_basic_set_is_empty(context_i)) {
 799                         isl_basic_set_free(context_i);
 800                         continue;
 801                 }
 802                 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
 803                                                 &bset->ineq[i]);
 804                 if (!upper || !context_i)
 805                         goto error;
 806                 if (fn(NULL, upper, context_i, user) < 0)
 807                         break;
 808         }
 809
 810         isl_basic_set_free(context);
 811
 812         if (i < bset->n_ineq)
 813                 return -1;
 814
 815         return 0;
 816 error:
 817         isl_constraint_free(upper);
 818         isl_basic_set_free(context_i);
 819         isl_basic_set_free(context);
 820         return -1;
 821 }
 822
 823 static int foreach_lower_bound(__isl_keep isl_basic_set *bset,
 824         enum isl_dim_type type, unsigned abs_pos,
 825         __isl_take isl_basic_set *context, int n_lower,
 826         int (*fn)(__isl_take isl_constraint *lower,
 827                   __isl_take isl_constraint *upper,
 828                   __isl_take isl_basic_set *bset, void *user), void *user)
 829 {
 830         isl_basic_set *context_i;
 831         isl_constraint *lower = NULL;
 832         int i;
 833
 834         for (i = 0; i < bset->n_ineq; ++i) {
 835                 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
 836                         continue;
 837
 838                 context_i = set_largest_lower_bound(context, bset,
 839                                                         abs_pos, n_lower, i);
 840                 if (isl_basic_set_is_empty(context_i)) {
 841                         isl_basic_set_free(context_i);
 842                         continue;
 843                 }
 844                 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
 845                                                 &bset->ineq[i]);
 846                 if (!lower || !context_i)
 847                         goto error;
 848                 if (fn(lower, NULL, context_i, user) < 0)
 849                         break;
 850         }
 851
 852         isl_basic_set_free(context);
 853
 854         if (i < bset->n_ineq)
 855                 return -1;
 856
 857         return 0;
 858 error:
 859         isl_constraint_free(lower);
 860         isl_basic_set_free(context_i);
 861         isl_basic_set_free(context);
 862         return -1;
 863 }
 864
 865 static int foreach_bound_pair(__isl_keep isl_basic_set *bset,
 866         enum isl_dim_type type, unsigned abs_pos,
 867         __isl_take isl_basic_set *context, int n_lower, int n_upper,
 868         int (*fn)(__isl_take isl_constraint *lower,
 869                   __isl_take isl_constraint *upper,
 870                   __isl_take isl_basic_set *bset, void *user), void *user)
 871 {
 872         isl_basic_set *context_i, *context_j;
 873         isl_constraint *lower = NULL;
 874         isl_constraint *upper = NULL;
 875         int i, j;
 876
 877         for (i = 0; i < bset->n_ineq; ++i) {
 878                 if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
 879                         continue;
 880
 881                 context_i = set_largest_lower_bound(context, bset,
 882                                                         abs_pos, n_lower, i);
 883                 if (isl_basic_set_is_empty(context_i)) {
 884                         isl_basic_set_free(context_i);
 885                         continue;
 886                 }
 887
 888                 for (j = 0; j < bset->n_ineq; ++j) {
 889                         if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
 890                                 continue;
 891
 892                         context_j = set_smallest_upper_bound(context_i, bset,
 893                                                             abs_pos, n_upper, j);
 894                         context_j = isl_basic_set_extend_constraints(context_j,
 895                                                                         0, 1);
 896                         context_j = add_larger_bound_constraint(context_j,
 897                                 bset->ineq[i], bset->ineq[j], abs_pos, 0);
 898                         context_j = isl_basic_set_simplify(context_j);
 899                         context_j = isl_basic_set_finalize(context_j);
 900                         if (isl_basic_set_is_empty(context_j)) {
 901                                 isl_basic_set_free(context_j);
 902                                 continue;
 903                         }
 904                         lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
 905                                                         &bset->ineq[i]);
 906                         upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
 907                                                         &bset->ineq[j]);
 908                         if (!lower || !upper || !context_j)
 909                                 goto error;
 910                         if (fn(lower, upper, context_j, user) < 0)
 911                                 break;
 912                 }
 913
 914                 isl_basic_set_free(context_i);
 915
 916                 if (j < bset->n_ineq)
 917                         break;
 918         }
 919
 920         isl_basic_set_free(context);
 921
 922         if (i < bset->n_ineq)
 923                 return -1;
 924
 925         return 0;
 926 error:
 927         isl_constraint_free(lower);
 928         isl_constraint_free(upper);
 929         isl_basic_set_free(context_i);
 930         isl_basic_set_free(context_j);
 931         isl_basic_set_free(context);
 932         return -1;
 933 }
 934
 935 /* For each pair of lower and upper bounds on the variable "pos"
 936  * of type "type", call "fn" with these lower and upper bounds and the
 937  * set of constraints on the remaining variables where these bounds
 938  * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
 939  *
 940  * If the designated variable is equal to an affine combination of the
 941  * other variables then fn is called with both lower and upper
 942  * set to the corresponding equality.
 943  *
 944  * If there is no lower (or upper) bound, then NULL is passed
 945  * as the corresponding bound.
 946  *
 947  * We first check if the variable is involved in any equality.
 948  * If not, we count the number of lower and upper bounds and
 949  * act accordingly.
 950  */
 951 int isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
 952         enum isl_dim_type type, unsigned pos,
 953         int (*fn)(__isl_take isl_constraint *lower,
 954                   __isl_take isl_constraint *upper,
 955                   __isl_take isl_basic_set *bset, void *user), void *user)
 956 {
 957         int i;
 958         isl_constraint *lower = NULL;
 959         isl_constraint *upper = NULL;
 960         isl_basic_set *context = NULL;
 961         unsigned abs_pos;
 962         int n_lower, n_upper;
 963
 964         if (!bset)
 965                 return -1;
 966         isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
 967         isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
 968                 return -1);
 969
 970         abs_pos = pos;
 971         if (type == isl_dim_set)
 972                 abs_pos += isl_basic_set_dim(bset, isl_dim_param);
 973
 974         for (i = 0; i < bset->n_eq; ++i) {
 975                 if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
 976                         continue;
 977
 978                 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
 979                                                 &bset->eq[i]);
 980                 upper = isl_constraint_copy(lower);
 981                 context = isl_basic_set_remove_dims(isl_basic_set_copy(bset),
 982                                         type, pos, 1);
 983                 if (!lower || !upper || !context)
 984                         goto error;
 985                 return fn(lower, upper, context, user);
 986         }
 987
 988         n_lower = 0;
 989         n_upper = 0;
 990         for (i = 0; i < bset->n_ineq; ++i) {
 991                 if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
 992                         n_lower++;
 993                 else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
 994                         n_upper++;
 995         }
 996
 997         context = isl_basic_set_copy(bset);
 998         context = isl_basic_set_cow(context);
 999         if (!context)
1000                 goto error;
1001         for (i = context->n_ineq - 1; i >= 0; --i)
1002                 if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
1003                         isl_basic_set_drop_inequality(context, i);
1004
1005         context = isl_basic_set_drop(context, type, pos, 1);
1006         if (!n_lower && !n_upper)
1007                 return fn(NULL, NULL, context, user);
1008         if (!n_lower)
1009                 return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
1010                                                 fn, user);
1011         if (!n_upper)
1012                 return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
1013                                                 fn, user);
1014         return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
1015                                         fn, user);
1016 error:
1017         isl_constraint_free(lower);
1018         isl_constraint_free(upper);
1019         isl_basic_set_free(context);
1020         return -1;
1021 }
1022
1023 __isl_give isl_aff *isl_constraint_get_bound(
1024         __isl_keep isl_constraint *constraint, enum isl_dim_type type, int pos)
1025 {
1026         isl_aff *aff;
1027         isl_local_space *ls;
1028
1029         if (!constraint)
1030                 return NULL;
1031         if (pos >= isl_basic_set_dim(constraint->bmap, type))
1032                 isl_die(constraint->ctx, isl_error_invalid,
1033                         "index out of bounds", return NULL);
1034         if (!isl_basic_map_may_be_set(constraint->bmap))
1035                 isl_die(constraint->ctx, isl_error_invalid,
1036                         "not a set constraint", return NULL);
1037
1038         pos += offset(constraint, type);
1039         if (isl_int_is_zero(constraint->line[0][pos]))
1040                 isl_die(constraint->ctx, isl_error_invalid,
1041                         "constraint does not define a bound on given dimension",
1042                         return NULL);
1043
1044         ls = isl_basic_set_get_local_space(constraint->bmap);
1045         aff = isl_aff_alloc(ls);
1046         if (!aff)
1047                 return NULL;
1048
1049         if (isl_int_is_neg(constraint->line[0][pos]))
1050                 isl_seq_cpy(aff->v->el + 1, constraint->line[0],
1051                             aff->v->size - 1);
1052         else
1053                 isl_seq_neg(aff->v->el + 1, constraint->line[0],
1054                             aff->v->size - 1);
1055         isl_int_set_si(aff->v->el[1 + pos], 0);
1056         isl_int_abs(aff->v->el[0], constraint->line[0][pos]);
1057
1058         return aff;
1059 }
1060
1061 /* For an inequality constraint
1062  *
1063  *      f >= 0
1064  *
1065  * or an equality constraint
1066  *
1067  *      f = 0
1068  *
1069  * return the affine expression f.
1070  */
1071 __isl_give isl_aff *isl_constraint_get_aff(
1072         __isl_keep isl_constraint *constraint)
1073 {
1074         isl_aff *aff;
1075         isl_local_space *ls;
1076
1077         if (!constraint)
1078                 return NULL;
1079
1080         ls = isl_basic_set_get_local_space(constraint->bmap);
1081         aff = isl_aff_alloc(ls);
1082         if (!aff)
1083                 return NULL;
1084
1085         isl_seq_cpy(aff->v->el + 1, constraint->line[0], aff->v->size - 1);
1086         isl_int_set_si(aff->v->el[0], 1);
1087
1088         return aff;
1089 }
1090
1091 /* Construct an equality constraint equating the given affine expression
1092  * to zero.
1093  */
1094 __isl_give isl_constraint *isl_equality_from_aff(__isl_take isl_aff *aff)
1095 {
1096         int k;
1097         isl_basic_set *bset;
1098
1099         if (!aff)
1100                 return NULL;
1101
1102         bset = isl_basic_set_from_local_space(isl_aff_get_local_space(aff));
1103         bset = isl_basic_set_extend_constraints(bset, 1, 0);
1104         k = isl_basic_set_alloc_equality(bset);
1105         if (k < 0)
1106                 goto error;
1107
1108         isl_seq_cpy(bset->eq[k], aff->v->el + 1, aff->v->size - 1);
1109         isl_aff_free(aff);
1110
1111         return isl_basic_set_constraint(bset, &bset->eq[k]);
1112 error:
1113         isl_aff_free(aff);
1114         isl_basic_set_free(bset);
1115         return NULL;
1116 }
1117
1118 /* Construct an inequality constraint enforcing the given affine expression
1119  * to be non-negative.
1120  */
1121 __isl_give isl_constraint *isl_inequality_from_aff(__isl_take isl_aff *aff)
1122 {
1123         int k;
1124         isl_basic_set *bset;
1125
1126         if (!aff)
1127                 return NULL;
1128
1129         bset = isl_basic_set_from_local_space(isl_aff_get_local_space(aff));
1130         bset = isl_basic_set_extend_constraints(bset, 0, 1);
1131         k = isl_basic_set_alloc_inequality(bset);
1132         if (k < 0)
1133                 goto error;
1134
1135         isl_seq_cpy(bset->ineq[k], aff->v->el + 1, aff->v->size - 1);
1136         isl_aff_free(aff);
1137
1138         return isl_basic_set_constraint(bset, &bset->ineq[k]);
1139 error:
1140         isl_aff_free(aff);
1141         isl_basic_set_free(bset);
1142         return NULL;
1143 }